Radar systems and similar technologies require high-fidelity waveforms to be transmitted and received for processing, for example, synthetic aperture radar (SAR) requires fine range resolution. An approach for achieving fine range resolution can comprise transmitting a very narrow pulse and sampling the returned echo. This approach, while simple in theory, has some practical limitations such as a very high peak transmitter power and a very high bandwidth for an analog-to-digital (A/D) converter.
Pulse compression is a radar technique for reducing peak transmitter power while maintaining a fixed average transmitter power by coding the transmitted waveform in such a manner as to be able to decode the received echo into the various constituents of the transmitted code. Some pulse compression schemes, such as binary and polyphase codes, can change the phase of the transmitted signal at regular sub-pulse intervals. The length of these sub-pulse intervals determines the achievable range resolution.
Another pulse compression scheme involves continuously varying the phase of the transmitted waveform. When this phase variation is quadratic (and, therefore, the frequency variation is linear), the method is referred to as linear FM pulse, or chirp pulse compression. Such a waveform is described by:y(t)=sin {φ(t)}, 0≦t≦τ  Eqn. 1
where for a linear FM pulse the phase function is described byφ(t)=2π(f0t−kt/2+kt2/2)+φ0  Eqn. 2where k is the linear chirp rate, τ is the pulse length, f0 is the starting frequency and φ0 is the starting phase of the waveform, respectively.
It is quite common for the signal path (channel) to exhibit frequency-dependent phase perturbations which render anomalies to the transmitted waveform signal. Such distortions can be compensated by equalization techniques, including pre-distortion of the waveform. The frequency-dependent phase errors of wideband radar linear frequency modulated (LFM) chirp signals can be mitigated in this manner with a look-up table, where the instantaneous frequency output of a frequency accumulator is used to select a phase compensation that is applied to the instantaneous phase output of the subsequent phase accumulator. Such an approach for implementing chirp pulse compression can utilize a direct-digital-synthesis (DDS) circuitry, system 400, of FIG. 4 to facilitate generation of y(f). A frequency accumulator component 402 includes an adder component 410 in series with a register component 415 and a feedback loop 418 from the output of register 415 to the input through adder component 410. The frequency accumulator circuit can accumulate, or integrate, the chirp rate constant, k, and can further add the accumulated k to a programmed starting frequency f0 (which has been loaded into register component 415) to facilitate provision of an output f(t)=f0+kt, the instantaneous frequency. The instantaneous frequency f(t) can be utilized as the input to phase accumulator component 404 where the linear frequency term f(t) can be integrated to provide an output for the instantaneous phase φ(t).
The combination of accumulator component 402 and accumulator component 404 are collectively known as a phase generator (PG). The instantaneous phase φ(t) output of phase accumulator component 404 can be applied as an address to a mapping device such as a look-up table read-only memory (ROM) component 450 which can contain one cycle of a sine waveform. The resulting output of ROM component 450 can take the form of Eqn. 1. The phase accumulator component 404 and ROM component 450 form a digital portion of a conventional DDS, with the addition of a frequency accumulator 402 at the input to provide for the changing frequency of the chirp generator. The output of look-up table ROM 450 can be fed through a digital-to-analog (DAC) converter component 460 to provide an analog signal (e.g., an analog chirp signal 490) for subsequent transmission by a radar system. The phase error correction look up table (PEC LUT) 435 can be an important part of most modem chirp synthesizers which compensate for one or more non-linearities in RF components of a radar.
The advantages of system 400 can include a waveform length independent of hardware configuration, ease of changing waveform parameters, a capability of generating a continuous, constant frequency (CW) sinusoid, and a small part count. To change waveform parameters, all that is required is to change the values for the starting frequency f0, the starting phase φ0, and the chirp rate k, the values all of which can be stored in registers (e.g., register component 415 and register 440). A pulse length, τ, is also programmable. If desired, these parameters may be changed on a pulse by pulse basis. Since a chirp radar system may sometimes require two waveforms, one for use during transmit and a second for use during receive, the wave form synthesizer (WFM) chirp generator of FIG. 4 may be used with the starting frequency and pulse duration for each pulse loaded into different registers to permit independent specification of the transmit and receive waveforms.
While the approach illustrated in FIG. 4 can mitigate frequency-dependent phase errors, it is unable to correctly mitigate another class of phase errors, namely time-dependent phase errors. Time-dependent phase errors can be introduced into the circuit provided in FIG. 4, where, for example, a time-dependent phase error can be a result of power droop in a radar system amplifier. Power droop can be of concern for an amplifier (e.g., a traveling wave tube amplifier (TWTA)) being utilized as part of a radio frequency (RF) amplification system. For example, without a constant voltage at the amplifier, an analog chirp waveform 490 may be deleteriously affected by subsequent processing equipment comprising a radar system, for example, the transmitted waveform may be of a different profile to that generated by system 400. Accordingly, for example, if a constant voltage cannot be maintained, then the SAR's Impulse Response (IPR) may be deleteriously affected, although, for all intents and purposes it appears that the hardware and/or software associated with the SAR system is operating correctly.